Estimation of vaccine efficacy in outbreaks of acute infectious diseases

In a previous paper we defined the efficacy of a vaccine as 1-beta 1/beta 0, where beta 0 is the instantaneous probability of transmission of infection to an unvaccinated person exposed to a single infectious person, and beta 1 is similarly defined for a vaccinated person. We showed that under the conditions of an outbreak of an acute, directly transmitted infectious disease in a homogeneous and randomly mixing population, an estimate of this measure of vaccine efficacy is 1-[1n(1-A1)/1n(1-A0)], where A0 and A1 are the observed final attack rates among unvaccinated and vaccinated persons, respectively. In the present work we present an approximation for the standard error of this estimator, accounting for both the sampling and process variation. We extend the results of our previous paper to a stratified population, where the strata correspond to different levels of susceptibility and may have different vaccination coverage. We also consider populations that consist of small units (for example, households) where individuals mix primarily in these units. In this case, definition of vaccine efficacy is in terms of the within-unit transmission probabilities and is estimable by using transmission models for infectious diseases. We apply the estimation methods described above to data from influenza and measles outbreaks. We also examine, via a stochastic simulation study, the robustness of the vaccine efficacy estimators under various population structures and mixing patterns.